Liu, Yue2017-03-142017-03-142016-12https://hdl.handle.net/11299/185156University of Minnesota Ph.D. dissertation. December 2016. Major: Electrical Engineering. Advisor: P. Paul Ruden. 1 computer file (PDF); ix, 122 pages.Recently, transition metal dichalcogenides and black phosphorus (BP) emerged as new 2D semiconductors due to the advantages of moderate energy band gap, high carrier mobility, ultra thin film and high anisotropy. Together with graphene, 2D materials have been utilized in the development of biomedical devices, touch screen and display technologies, and flexible applications such as wearable electronics and IoT devices. They also open up new opportunities in research fields including spintronics, optoelectronics and next generation post-silicon transistor. In this dissertation, we present theoretical modeling for several topics related to 2D materials. Starting with the fundamental tight-binding theory of graphene, we review electronic properties for graphene including massless 2x2 Dirac Hamiltonian and pseudo-spin wave function. Followed by discussion of ballistic transport, a detailed analysis on graphene diffusive transport is provided. Ionized impurity scattering and carrier screening effect is considered in the model. The momentum relaxation time and mobility for graphene is modeled. A non-linear Thomas Fermi screening is introduced to improve the simulation accuracy. Taking the real spin into account, the new Hamiltonian is a 4x4 matrix. An external field perpendicular to the graphene breaks the reflection symmetry and introduces a Rashba spin-orbit interaction, which couples pseudo-spin and real spin. The relevant charge carrier states are no longer spin eigenstates. Rashba interaction is found to be quite small compared to Coulomb impurity scattering. To characterize the spin-polarized electrons tunneling from electrodes and transport in graphene, a spin valve device modeling and magnetoresistance calculation is developed. Black phosphorus possesses excellent properties like other 2D materials for high performance nanoelectronic applications. Moreover, there is a uniquely high in-plane anisotropy in BP due to its puckered crystal structure. To model the anisotropic transport, a model based on the BTE is developed, considering the full anisotropic electronic structure. For zero temperature calculation with ionized impurity limited scattering, anisotropy ratio 3-4 can be obtained from the model. Due to the dominating effect of screening, mobility is found to decrease weakly with increasing temperature. For , a smaller anisotropy ratio of 1.8-3.5 matching experimental measurements indicates that impurity scattering is an important mechanism for black phosphorus.en2D materialsblack phosphorusgraphenemodelingspintransportThesis or Dissertation